The Field of Reals is not omega-Automatic

Faried Abu Zaid, Erich GräDel & Lukasz Kaiser
We investigate structural properties of omega-automatic presentations of infinite structures in order to sharpen our methods to determine whether a given structure is omega-automatic. We apply these methods to show that no field of characteristic 0 admits an injective omega-automatic presentation, and that uncountable fields with a definable linear order cannot be omega-automatic.